This paper presents a general method using kernel Canonical Correlation Analysis (KCCA) to learn a semantic representation of web images and their associated text. The semantic space provides a common representation that enables comparison between text and images. The authors compare two approaches for retrieving images based on content from text queries against the Generalised Vector Space Model (GVSM). The paper reviews several methods for learning feature spaces, including Principal Component Analysis (PCA), Independent Component Analysis (ICA), Partial Least Squares (PLS), and Canonical Correlation Analysis (CCA). CCA is particularly effective for finding linear relationships between two sets of variables and is closely related to mutual information. KCCA extends CCA by mapping data to a higher-dimensional feature space using kernel methods, allowing for more flexible feature selection. The authors propose a general approach using KCCA for content-based and mate-based retrieval. They show that the general approach can be adapted to different types of problems by changing the selection of eigenvectors used in the semantic projection. They also explore a method for selecting the regularization parameter a priori to ensure good performance across different tasks. The paper discusses computational issues, including the use of large training sets and the need for dimensionality reduction. They introduce partial Gram-Schmidt orthogonolisation and incomplete Cholesky decomposition to address these issues. They show that partial Gram-Schmidt orthogonolisation is equivalent to incomplete Cholesky decomposition. The authors present experimental results comparing the performance of their method with the GVSM. They find that KCCA significantly outperforms GVSM in both content-based and mate-based retrieval. They also show that the a priori selection of the regularization parameter κ performs well, with only slight differences between the actual optimal κ and the a priori value. The paper concludes that KCCA provides a powerful method for learning semantic representations of multimedia content and is effective for both content-based and mate-based retrieval. The generalisation of CCA to more than two sets of variables is also discussed, preserving most of its properties.This paper presents a general method using kernel Canonical Correlation Analysis (KCCA) to learn a semantic representation of web images and their associated text. The semantic space provides a common representation that enables comparison between text and images. The authors compare two approaches for retrieving images based on content from text queries against the Generalised Vector Space Model (GVSM). The paper reviews several methods for learning feature spaces, including Principal Component Analysis (PCA), Independent Component Analysis (ICA), Partial Least Squares (PLS), and Canonical Correlation Analysis (CCA). CCA is particularly effective for finding linear relationships between two sets of variables and is closely related to mutual information. KCCA extends CCA by mapping data to a higher-dimensional feature space using kernel methods, allowing for more flexible feature selection. The authors propose a general approach using KCCA for content-based and mate-based retrieval. They show that the general approach can be adapted to different types of problems by changing the selection of eigenvectors used in the semantic projection. They also explore a method for selecting the regularization parameter a priori to ensure good performance across different tasks. The paper discusses computational issues, including the use of large training sets and the need for dimensionality reduction. They introduce partial Gram-Schmidt orthogonolisation and incomplete Cholesky decomposition to address these issues. They show that partial Gram-Schmidt orthogonolisation is equivalent to incomplete Cholesky decomposition. The authors present experimental results comparing the performance of their method with the GVSM. They find that KCCA significantly outperforms GVSM in both content-based and mate-based retrieval. They also show that the a priori selection of the regularization parameter κ performs well, with only slight differences between the actual optimal κ and the a priori value. The paper concludes that KCCA provides a powerful method for learning semantic representations of multimedia content and is effective for both content-based and mate-based retrieval. The generalisation of CCA to more than two sets of variables is also discussed, preserving most of its properties.